   Chapter 11.4, Problem 38E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Water depth Water is flowing into a barrel in the shape of a right circular cylinder at the rate of 200 in 3 /min . If the radius of the barrel is 18 in., at what rate is the depth of the water changing when the water is 30 in. deep?

To determine

To calculate: The rate at which the depth of water is changing when the water is 30 in. deep and the water is flowing into a barrel in the shape of a right circular cylinder at the rate of 200 in3/min. and the radius of barrel is 18 in.

Explanation

Given Information:

The water is 30 in. deep and the water is flowing into a barrel in the shape of a right circular cylinder at the rate of 200 in3/min. and the radius of barrel is 18 in..

Formula used:

The volume of a right circular cylinder with radius r is given by,

V=πr2h

According to the chain rule differentiation, if y=f(u), where u=g(x), then y is a differentiable function of x.

dydx=dydududx

The derivative of a constant value, k, is

ddx(k)=0

Calculation:

The volume of a right circular cylinder with radius r is given by,

V=πr2h

Now, as provided that radius is 18 in

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